In other words, I'm now looking for cases in which a woodworker eventually might own two or more of a given tool, but keeping more than one of them is difficult to justify objectively because having more than one provides little or no practical benefit.

Unfortunately, this turns out to much more difficult than I had originally thought, because one most prove that there is NO situation in which the tool is useful in multiples. As it turns out, it's very difficult (or impossible, in many cases) to prove this objectively.

Instead of trying to create a list of tools that are not useful in multiples, what factors should I consider in order to determine whether or not I should limit myself to just one of a given tool?

2 Answers
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No single specific answer will apply to everyone.

Trying to enumerate the tools that aren't useful in multiples doesn't seem helpful — there are as many valid answers as there are woodworkers. Instead, then, let's consider the criteria that anyone can use to decide whether they need more than one (or zero, two, three, or ten) of a given tool, or conversely, when they don't need more than some number of that tool.

The cost of a tool should be less than the benefit derived from the tool.

The cost of a tool is more than just the purchase price. Every tool takes up some amount of space and many require a certain amount of maintenance.

The primary benefit of a tool is usually that it facilitates some task, but there's also the pleasure of ownership and sometimes the security or convenience of having an extra copy of the tool.

For most tools, the main benefit of owning more than one copy is time.

You can only use one table saw, router, hammer, or 1/8" chisel tip drill bit at a time, so having more than one isn't necessary but might be convenient. Anything that can be done with two routers can be done with one, but having more than one lets you keep one in a router table or use multiple cutters without changing setups. It's hard to swing two hammers at the same time, but having one in the shop, one in your truck, and your tool bucket saves the trouble of moving a single hammer to different sites.

The higher a tool's cost, the harder it is to justify multiples.

It'd be cool to have a second table saw that's always set up for dadoes, but I can't afford to give up that much space in my small shop. This is a case where the convenience of two doesn't match the cost.

It's harder to justify multiples if they can't be used simultaneously.

Clamps are useful in multiples because they're used in parallel. They're more like fixtures than tools in that they do their work after you've operated them. Most tools are useful while they're being operated, which makes it hard for a single woodworker to benefit from more than one at a time. On the other hand, if you ever work with other people, multiples might make a lot of sense.

It's harder to justify multiples of tools that are seldom used.

If a tool isn't used often, you might not even need one, let alone several. A single adjustable finger dovetail jig can be useful enough to justify the cost even if you only use it a few times a year, but a second adjustable finger dovetail jig really doesn't provide any extra utility.

There are a few main things to look at whether a tool is worth having in multiples. For many, especially amateur woodworkers, space is going to be the primary consideration. While it might be 'convenient' to have 4 bandsaws each with a different blade so you don't have to change them all the time, they will take up a lot of space that can be used for other things. If you are a production shop, it might actually make sense to have more than one, because of the time savings of not having to keep changing blades.

The second (maybe first) biggest issue is cost. Having 3 table saws (while also a huge space hog) to have different set ups Dado's, ripping, large flat material, etc. can be expensive. Most woodworkers have to save up to get themselves 1 decent table saw. They might have two if they bought a cheap one to get the job done until they could buy a good one, but whether they keep it, is both space (is there room for two?) and money (Can I sell the old one to help pay for the new one?)

The next considerations would be: Why do you need multiples?

Answers.
If each one is, or can be dedicated to specific work, such as one table saw dedicated to the Dado stack. This might be to help keep set up and tear down times to a minimum. If you find yourself switching the blades back and forth a lot this might be a reason. (also just doing a better job of organizing your cuts could help!)

Do they actually DO different things? Hammers are a ubiquitous tool and a generic name. You can have a dozen different hammers and each one could have a different and unique application. While many can be used for multiple applications, how specialized you are at specific tasks would determine if you need certain special tools, or if the old standby can work.

How many people are going to need to use the tools? In a shop of 1, chances are you can generally only use one at a time, so you will likely only need multiples of tools when dedicating one or more to specific tasks for time saving processes (such as having 2-3 drills to avoid changing drill, countersink and driver). Sharing shops or tools among several wood workers would more likely be to have multiples of the tools that cause the most contention. If people are always waiting for the table saw, buying a second would seem to be a good idea (money and space allowing).